Error estimates of a high order numerical method for solving linear fractional differential equations
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Luliang University; University of ChesterPublication Date
2016-04-29
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In this paper, we first introduce an alternative proof of the error estimates of the numerical methods for solving linear fractional differential equations proposed in Diethelm [6] where a first-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and the convergence order of the proposed numerical method is O(∆t 2−α ), 0 < α < 1, where α is the order of the fractional derivative and ∆t is the step size. We then use the similar idea to prove the error estimates of a high order numerical method for solving linear fractional differential equations proposed in Yan et al. [37], where a second-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and we show that the convergence order of the numerical method is O(∆t 3−α ), 0 < α < 1. The numerical examples are given to show that the numerical results are consistent with the theoretical results.Citation
Li, Z., Yan, Y., & Ford, N. J. (2016). Error estimates of a high order numerical method for solving linear fractional differential equations. Applied Numerical Mathematics, 114, 201-220. https://doi.org/10.1016/j.apnum.2016.04.010Publisher
ElsevierJournal
Applied Numerical MathematicsAdditional Links
http://www.journals.elsevier.com/applied-numerical-mathematics/Type
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enEISSN
1873-5460ae974a485f413a2113503eed53cd6c53
10.1016/j.apnum.2016.04.010
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